Preheat oven to 375 degrees F. Lightly grease a baking sheet or line with parchment paper.
In the bowl of a stand mixer, cream the butter, sugar, and cream cheese until light and fluffy using the whisk attachment. Mix in the corn syrup, vanilla, almond extract, and egg, scraping the sides and bottom of the bowl so that everything gets mixed in.
Switch your mixer attachment to a paddle or dough hook. Mix in flour, baking powder, salt, and baking soda until everything is mixed in.
Pinch off 1 tablespoon of dough. Roll into a ball and gently press between hands or fingers to flatten. Repeat with remaining dough.
Place cookies on the prepared baking sheet. Bake in the preheated oven for 10 minutes. Remove from oven and cool for 2 to 3 minutes on the pan before carefully removing to cool completely on a cooling rack.
To make the frosting, cream butter with a hand mixer in a large mixing bowl until light and fluffy. Beat in vanilla extract. Slowly add in powdered sugar, 1 cup at a time, mixing in between until thick. Use milk as needed to thin out. Dye with food coloring if desired.
Frost cookies once completely cooled. Store in an airtight container.